Doping-tunable thermal emission from plasmon polaritons in semiconductor epsilon- near-zero thin films
Young Chul Jun, Ting S. Luk, A. Robert Ellis, John F. Klem, and Igal Brener
Citation: Applied Physics Letters 105, 131109 (2014); doi: 10.1063/1.4896573 View online: http://dx.doi.org/10.1063/1.4896573
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/105/13?ver=pdfcov Published by the AIP Publishing
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Doping-tunable thermal emission from plasmon polaritons in semiconductor epsilon-near-zero thin films
Young Chul Jun,1,a)Ting S. Luk,2,3,b)A. Robert Ellis,3John F. Klem,3and Igal Brener2,3
1Department of Physics, Inha University, Incheon 402-751, South Korea
2Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
3Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
(Received 10 September 2014; accepted 14 September 2014; published online 30 September 2014) We utilize the unique dispersion properties of leaky plasmon polaritons in epsilon-near-zero (ENZ) thin films to demonstrate thermal radiation control. Owing to its highly flat dispersion above the light line, a thermally excited leaky wave at the ENZ frequency out-couples into free space without any scattering structures, resulting in a narrowband, wide-angle, p-polarized thermal emission spec- trum. We demonstrate this idea by measuring angle- and polarization-resolved thermal emission spectra from a single layer of unpatterned, doped semiconductors with deep-subwavelength film thickness (d=k0 6103, wheredis the film thickness and k0 is the free space wavelength).
We show that this semiconductor ENZ film effectively works as a leaky wave thermal radiation antenna, which generates far-field radiation from a thermally excited mode. The use of semicon- ductors makes the radiation frequency highly tunable by controlling doping densities and also facil- itates device integration with other components. Therefore, this leaky plasmon polariton emission from semiconductor ENZ films provides an avenue for on-chip control of thermal radiation.
VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4896573]
Control of thermal radiation has been intensively studied for important energy conversion applications such as thermo- photovoltaics and infrared (IR) sources. Surface gratings or resonant structures have been adopted to alter thermal radia- tion properties and achieve spectrally selective thermal emis- sion.1–14 In such patterns, narrowband thermal emission could be obtained at desired frequencies, which are deter- mined by the pattern geometry. In addition, it is possible to get directional thermal emission by adjusting the scattering properties of structured surfaces.3,11 Especially, surface waves are useful for engineering the properties of thermal radiation. Surface phonon polaritons on SiC and surface plasmon polaritons on metals or doped semiconductors have been used to tailor angular and spectral properties of thermal emission. However, these surface waves still need scatterers or antenna structures to convert them to far-field radiation.
Recently, there have been interesting studies on transverse-magnetic (TM) waveguide modes near the epsilon zero frequency of a material.15–18 Ultra-thin materials can support both leaky and bound modes around the epsilon- near-zero (ENZ) frequency with highly flat dispersion. The leaky waves in ENZ films correspond to what has been called Berreman absorption19 and can naturally out-couple into free space without any surface patterning. Here, we uti- lize the unique optical properties of these leaky waves in ENZ films and demonstrate spectrally selective thermal emission. Unlike previous studies on structured surfaces, we employ an unpatterned, doped semiconductor layer with a deep-subwavelength film thickness (dk0, whered is the film thickness and k0 is the free space wavelength). These
doped semiconductor thin films support leaky plasmon polar- iton modes at the ENZ frequency, which can be thermally excited and out-coupled to the far field without any scatter- ing structures. This leaky plasmon polaritons emission mani- fests its highly flat dispersion characteristics; it produces a narrowband, wide-angle, p-polarized thermal emission spec- trum. We experimentally verify this idea through the direct measurement of angle- and polarization-resolved thermal emission spectra.
There have been several studies on thermal emission control from planar structures in the past.20–22 But those studies employed a complicated multilayer stack to form Fabry-Perot resonators or one-dimensional photonic crystals.
Recently, there was also a theoretical study on thermal emis- sion from ENZ metamaterials consisting of metal-dielectric multi-layer stacks or metal nanowire arrays.23In contrast, in our work, we use a single layer of ultra-thin, doped semicon- ductor and clarify the role of leaky modes existing in such ENZ thin films. The use of semiconductors makes the ther- mal radiation frequency (i.e., ENZ frequency) easily tunable during the material growth by controlling doping densities. It also facilitates device integration with other chip compo- nents. Therefore, leaky modes of semiconductor ENZ films can be a useful tool for on-chip control of thermal radiation.
Figure 1(a) shows a schematic of the sample structure studied here. A doped semiconductor thin film is grown on an undoped substrate, and the sample is heated on a hot plate. The leaky plasmon polariton mode in the doped semi- conductor layer is thermally excited and out-couples to the far field, generating a narrowband thermal emission spec- trum from an unpatterned film.
To understand the physical nature of this leaky mode, we first examine the dispersion properties of the different op- tical modes in doped-semiconductor ENZ thin films. The
a)youngchul.jun@inha.ac.kr,
b)tsluk@sandia.gov
0003-6951/2014/105(13)/131109/5/$30.00 105, 131109-1 VC2014 AIP Publishing LLC
dielectric constant e of a semiconductor material can be modeled using the Drude approximation
e¼e1 1 x2p x2þixC
!
; (1)
wherexp ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Nq2=ðe0e1mÞ
p is the plasma frequency,e1is the high frequency dielectric constant,xis the angular fre- quency of incident light,Nis the electron density,m*is the electron effective mass, andCis the damping coefficient. In doped semiconductors, the frequency where the real part of the dielectric constant (Re[e]) becomes zero can be con- trolled by adjusting the doping density (the doping densityN affects the plasma frequency and, in turn, the dielectric con- stante). The dispersion relation for p-polarized modes in an asymmetric three-layer structure can be obtained by numeri- cally solving the following relation:
1þe1kz3
e3kz1
¼i tanðkz2dÞ e2kz3
e3kz2
þe1kz2
e2kz1
; (2)
wherekzn¼ ðenx2=c2k2jjÞ1=2. We calculated the dispersion relations for an [air/nþInAs/substrate] structure for several ENZ layer (i.e., nþInAs) thicknesses. We assumed undoped GaAs as our substrate and used the dielectric constants obtained by ellipsometry measurements. In Fig. 1(b), the doping density is ND¼1.11019cm3 and the ENZ fre- quency is1080 cm1 (the horizontal dashed line). In Fig.
1(c), the doping density is ND¼5.61018cm3 and the ENZ frequency is reduced to870 cm1. In both cases, the dispersion curves are divided into two branches; one is on the left side of the light line (i.e., leaky modes) and are called Berreman modes, and the other is on the right side of the light line (i.e., bound modes) and are called ENZ modes.15 As the ENZ layer thickness d decreases, both modes approach the epsilon zero frequency (Re[e]¼0), and the dis- persion curves become highly flat. Because there is no mode cutoff as the film thickness is decreased, these modes can even exist in films with truly nanoscale thicknesses. The mode properties are mainly determined by the ENZ layer itself (i.e., doped semiconductor); similar Berreman and ENZ modes even exist on a metal substrate, and the mode dispersion relations do not change significantly.
ENZ modes are bound modes, and thus cannot couple to free space optical modes without a scattering or antenna structure. However, Berreman modes are leaky modes and will couple to free space even when excited thermally.
Furthermore, for thin films, the Berreman mode dispersion becomes highly flat. Therefore, this leaky radiation should be spectrally narrow. At the same time, it should be strongly p-polarized because it originates from a p-polarized mode.
We utilize these unique properties of Berreman modes to demonstrate p-polarized, narrowband, doping-tunable ther- mal radiation from unpatterned, ultra-thin semiconductor films.
We prepared two semiconductor wafers (wafers A and B) grown using molecular beam epitaxy (MBE). Undoped 100 nm GaAs and 1000 nm AlSb buffer epilayers were first grown on a semi-insulating GaAs substrate, followed by the growth of a 60 nm nþInAs epilayer and a 30 nm undoped InAs cap layer. In wafer A, the doping density of nþInAs ENZ layer was ND¼1.11019cm3, and in wafer B, ND¼5.61018cm3. These doping densities were deter- mined by Hall measurements after wafer growth.
The wafers were first characterized by optical absorption measurements. Because Berreman modes can be excited by free-space coupling of light, the absorption spectrum should exhibit these spectral features. To verify this, we performed hemispherical directional reflectometer (HDR) measure- ments (Surface Optics SOC-100) with a broadband thermal IR source. The reflectivity and transmissivity spectra of the samples were measured at room temperature for different incident angles to obtain absorptivity (A¼1 –R–T). Figure 2shows the measured absorption spectra from wafers A and B. These measurements were repeated by varying the inci- dence angle in 15 increments, and thus we obtained angle- resolved absorption spectra for p- and s-polarizations of the incident light. As we expected from the properties of Berreman modes, we have strong absorption peaks around the ENZ frequency in the p-polarized spectra. In wafer A (ND¼1.11019cm3), strong absorption peaks appeared around 1080 cm1 in the p-polarized spectra at all angles (Fig. 2(a)). However, in the s-polarized spectra (Fig. 2(b)), there were only very weak features around the ENZ fre- quency. In wafer B (ND¼5.61018cm3), the ENZ fre- quency is at a lower frequency (around 870 cm1) due to the
FIG. 1. (a) Schematic of leaky wave thermal emission. The sample including an ultra-thin doped semiconductor layer is heated using a hot plate. Thermally excited leaky modes are naturally out-coupled to far-field, generating a narrowband thermal emission spectrum at the ENZ frequency. (b) and (c) Dispersion relations of Berreman and ENZ modes for two different InAs doping densities: (b) ND¼1.11019cm3, (c) ND¼5.61018cm3. Dotted black lines are the light line in air.
131109-2 Junet al. Appl. Phys. Lett.105, 131109 (2014)
reduced doping density. Again, the p-polarized spectra showed clear absorption peaks (Fig. 2(c)), while the s- polarized spectra had very weak features (Fig.2(d)). These absorption features agree well with the dispersion properties that we discussed above. We also measured absorption spec- tra of a bare GaAs substrate for comparison, and there were no sharp features for both polarizations (Figs.2(e)and2(f)).
We can easily understand this from the fact that Berreman modes do not exist in such undoped substrate.
According to Kirchhoff’s law of thermal radiation, the absorptivity of an object should be equal to its emissivity (A¼¾) for each frequency and each incident angle at ther- mal equilibrium. Therefore, we expect to obtain narrow- band thermal emission spectra from these samples. Due to Kirchhoff’s law, emissivity is often deduced from reflectiv- ity and transmissivity measurements. However, standard reflectivity and transmissivity measurements often fail to detect scattered light from a sample. We avoid such inac- curacies by directly measuring thermal emission spectra as a function of angle. Furthermore, we also perform accurate background correction by placing a well-calibrated refer- ence material together with the sample in a thermally uni- form environment.24,25 Figure 3 shows a schematic of the setup for our angle- and polarization-resolved thermal emission measurements. It consists of a vacuum chamber attached to a Fourier-transform infrared spectrometer
(FTIR). We performed FTIR external source mode meas- urements. The sample and reference materials were heated to 140C using a hot plate inside the vacuum chamber, and thermal emission spectra were measured for different sam- ple tilt angles. For each measurement, the polarization of the incident light was varied to be either p- or s-polarized.
Figure 4 shows the measured emissivity spectra from wafers A and B. For these emission spectra, thermal emis- sion spectra exhibit a clear difference between p- and s-polarizations. Only p-polarized spectra show very sharp thermal emission peaks around the ENZ frequency. In wafer A, the emission peak appeared around 1050 cm1(Fig.4(a)), superimposed on a feature-less background emission spec- trum that corresponds to the bulk GaAs substrate. It is worth noticing that even though we have an ultra-thin, doped semi- conductor layer, we observe a clear emission peak. Here, the film thickness (60 nm) corresponds to d=k0 6103, wheredis the film thickness and k0 is the free space wave- length. In wafer B, the peak again appears at a lower fre- quency (around 850 cm1) due to the reduced doping density (Fig.4(c)). In both wafers, there are only much weaker fea- tures in the s-polarized emissivity spectra (Figs. 4(b) and 4(d)). As expected, there is a very clear contrast between the p- and s-polarization measurements. The peak positions are similar to those in the absorption spectra, but they are slightly red-shifted due to the elevated temperature for ther- mal measurements.26We also measured the thermal emissiv- ity of a bare GaAs substrate. The bare substrate gives no features around the ENZ frequency for both p- and s- polarizations. Bulk GaAs emission could be eliminated by removing the carrier substrate and transferring the doped layer to a low-emissivity substrate. Or, the doped layer could be grown on a low-emissivity substrate from the beginning.
An emissivity close to one can be also achieved if the undoped GaAs is replaced with metal (e.g., see the perfect absorption scheme in Ref.27).
Our measurements clearly show that unpatterned semi- conductor thin films generate spectrally selective thermal emission near the ENZ frequencies that are determined purely by doping densities. Thermally excited Berreman modes in the doped semiconductor radiate to free space due to the leaky nature of the Berreman modes. Thus, an
FIG. 2. Angle-resolved, polarization-dependent absorptivity measurements for p- and s-polarizations. (a) and (b) Wafer A (60 nm nþ InAs, ND¼1.11019cm3): we have strong absorption peaks around the ENZ frequency in the p-polarized spectra. (c) and (d) Wafer B (60 nm nþInAs, ND¼5.61018cm3): the ENZ peak in the p-polarized spectrum moves to a lower frequency due to the reduced doping level. All these features mani- fest optical characteristics of Berreman modes in doped semiconductor thin films. (e) and (f) The absorption spectra of an undoped GaAs substrate are also shown for comparison.
FIG. 3. Schematic of the setup for angle- and polarization-resolved thermal emission measurements.
ultra-thin ENZ film effectively works as a leaky wave ther- mal antenna,6,10which converts a thermally excited mode to far-field radiation. Some of the early studies of Berreman modes were done under thermal excitation followed by emis- sion measurements,28 but they were limited to phonon- polariton Berreman modes, where the mode frequency is
fixed by the optical phonons in the material. Here, we utilize plasmon polariton Berreman modes, where the emission can be tuned simply by changing the doping density. We used unpatterned, doped semiconductors with properties (mate- rial, doping level, thickness, etc.) that can be directly con- trolled during the growth process. Therefore, this can greatly simplify the device structure and fabrication for thermal radi- ation control. The use of semiconductors also facilitates de- vice integration with other chip components. Therefore, the leaky wave thermal emission from doped semiconductor films can be a useful tool for on-chip control of thermal radi- ation, such as energy conversion and thermal management (chip cooling). A doped semiconductor layer can be also used as an electrical current channel, and it could be possible to heat a sample electrically without a bulky hot plate. This can be useful for implementing chip-scale thermal emitters at IR frequencies where efficient sources are less readily available.
Finally, we performed numerical calculations and com- pared them with the Berreman mode dispersion. For an [air/
ENZ film (nþ InAs, ND¼1.11019cm3)/undoped GaAs substrate] structure, we calculated reflectivity (R) and transmissivity (T) numerically (using the transfer matrix method) and obtained absorptivity (A¼1 –R–T). Following Kirchhoff’s law, emissivity should be the same as absorptiv- ity. Figures 5(a) and 5(c) show absorptivity colormaps for p-polarized light incident from the air side. Absorptivity is plotted as a function of frequency and incidence angle. In Fig.5(a), the nþInAs layer thickness is d¼60 nm, and for Fig.5(c), d¼500 nm. Both show strong absorption near the ENZ frequency (1080 cm1). The thicker ENZ film has larger absorptivity, but the absorption peak is also broadened in the frequency domain (Fig.5(c)). Berreman mode disper- sion curves are also drawn in dotted white lines. We can see that absorption maxima occur along the Berreman mode dis- persion curve exactly in both cases. S-polarized light pro- duces completely different absorption behavior; Figures5(b) and 5(d) show absorptivity colormaps for s-polarization
FIG. 4. Angle-resolved, polarization-dependent emissivity measurements for p- and s-polarizations at 140C. (a) and (b) Wafer A (60 nm nþInAs, ND¼1.11019cm3): p-polarized spectra show very sharp thermal emis- sion peaks around the ENZ frequency. (c) and (d) Wafer B (60 nm nþInAs, ND¼5.61018cm3): the peaks appear at a lower frequency due to the reduced doping density. (e) and (f) Thermal emissivity spectra from an undoped GaAs substrate.
FIG. 5. Absorptivity calculation for an [air/ENZ/substrate] structure. (a) and (c) Strong absorption is observed near the ENZ frequency for p-polarized incident light. The Berreman mode dis- persion relations are also shown in dot- ted white lines. In a thinner film (d¼60 nm), the Berreman mode dis- persion is highly flat, while it is directed slightly upward in a thicker film (d¼500 nm). In both cases, absorption maxima occur along the Berreman mode dispersion curve. (b) and (d) Absorptivity calculation for s- polarization. Absorption is much weaker for s-polarization, and there are no narrowband features. Note that the color scale is different for each plot.
131109-4 Junet al. Appl. Phys. Lett.105, 131109 (2014)
(d¼60 nm for (b), d¼500 nm for (d)). Absorption is much weaker for s-polarization, and there are no narrowband fea- tures like those for p-polarization. These results agree well with our experiment results and confirm that our narrow- band, p-polarized thermal emission originates from the leaky modes existing in ENZ thin films.
In summary, we utilized the unique optical properties of leaky plasmon polaritons modes in ENZ thin films and dem- onstrated spectrally selective thermal emission. We explained the thermal emission properties of doped semiconductor thin films in terms of the mode characteristics. Thermally excited leaky waves in unpatterned semiconductor films naturally out- couple into free space, and thus result in narrowband, wide- angle, p-polarized thermal emission spectra following the highly flat mode dispersion characteristics. We verified this idea through the direct measurements of angle-resolved and polarization-resolved thermal emission spectra. The unique properties of the leaky wave emission could lead to chip- scale, easy-to-fabricate thermal emitters operating throughout the entire IR frequency range.
This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Sandia National Laboratories is a multi- program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under Contract DE-AC04- 94AL85000. Parts of this work were supported by the U.S.
Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering. Y.C.J.
acknowledges the supports from Inha University Research Grant (INHA-47839) and the National Research Foundation of Korea (NRF) grant funded by the Korea government (Ministry of Science, ICT and Future Planning; No. 2008- 0061893).
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